cart-elc

Source code for CART-ELC
git clone git://git.laack.co/cart-elc.git
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eigensolver_complex.cpp (6221B)

      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
      5 // Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
      6 //
      7 // This Source Code Form is subject to the terms of the Mozilla
      8 // Public License v. 2.0. If a copy of the MPL was not distributed
      9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
     10 
     11 #include "main.h"
     12 #include <limits>
     13 #include <Eigen/Eigenvalues>
     14 #include <Eigen/LU>
     15 
     16 template<typename MatrixType> bool find_pivot(typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0)
     17 {
     18   bool match = diffs.diagonal().sum() <= tol;
     19   if(match || col==diffs.cols())
     20   {
     21     return match;
     22   }
     23   else
     24   {
     25     Index n = diffs.cols();
     26     std::vector<std::pair<Index,Index> > transpositions;
     27     for(Index i=col; i<n; ++i)
     28     {
     29       Index best_index(0);
     30       if(diffs.col(col).segment(col,n-i).minCoeff(&best_index) > tol)
     31         break;
     32       
     33       best_index += col;
     34       
     35       diffs.row(col).swap(diffs.row(best_index));
     36       if(find_pivot(tol,diffs,col+1)) return true;
     37       diffs.row(col).swap(diffs.row(best_index));
     38       
     39       // move current pivot to the end
     40       diffs.row(n-(i-col)-1).swap(diffs.row(best_index));
     41       transpositions.push_back(std::pair<Index,Index>(n-(i-col)-1,best_index));
     42     }
     43     // restore
     44     for(Index k=transpositions.size()-1; k>=0; --k)
     45       diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second));
     46   }
     47   return false;
     48 }
     49 
     50 /* Check that two column vectors are approximately equal up to permutations.
     51  * Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(),
     52  * however this strategy is numerically inacurate because of numerical cancellation issues.
     53  */
     54 template<typename VectorType>
     55 void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
     56 {
     57   typedef typename VectorType::Scalar Scalar;
     58   typedef typename NumTraits<Scalar>::Real RealScalar;
     59 
     60   VERIFY(vec1.cols() == 1);
     61   VERIFY(vec2.cols() == 1);
     62   VERIFY(vec1.rows() == vec2.rows());
     63   
     64   Index n = vec1.rows();
     65   RealScalar tol = test_precision<RealScalar>()*test_precision<RealScalar>()*numext::maxi(vec1.squaredNorm(),vec2.squaredNorm());
     66   Matrix<RealScalar,Dynamic,Dynamic> diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2();
     67   
     68   VERIFY( find_pivot(tol, diffs) );
     69 }
     70 
     71 
     72 template<typename MatrixType> void eigensolver(const MatrixType& m)
     73 {
     74   /* this test covers the following files:
     75      ComplexEigenSolver.h, and indirectly ComplexSchur.h
     76   */
     77   Index rows = m.rows();
     78   Index cols = m.cols();
     79 
     80   typedef typename MatrixType::Scalar Scalar;
     81   typedef typename NumTraits<Scalar>::Real RealScalar;
     82 
     83   MatrixType a = MatrixType::Random(rows,cols);
     84   MatrixType symmA =  a.adjoint() * a;
     85 
     86   ComplexEigenSolver<MatrixType> ei0(symmA);
     87   VERIFY_IS_EQUAL(ei0.info(), Success);
     88   VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
     89 
     90   ComplexEigenSolver<MatrixType> ei1(a);
     91   VERIFY_IS_EQUAL(ei1.info(), Success);
     92   VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
     93   // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
     94   // another algorithm so results may differ slightly
     95   verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
     96 
     97   ComplexEigenSolver<MatrixType> ei2;
     98   ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
     99   VERIFY_IS_EQUAL(ei2.info(), Success);
    100   VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
    101   VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
    102   if (rows > 2) {
    103     ei2.setMaxIterations(1).compute(a);
    104     VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
    105     VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
    106   }
    107 
    108   ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
    109   VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
    110   VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
    111 
    112   // Regression test for issue #66
    113   MatrixType z = MatrixType::Zero(rows,cols);
    114   ComplexEigenSolver<MatrixType> eiz(z);
    115   VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
    116 
    117   MatrixType id = MatrixType::Identity(rows, cols);
    118   VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
    119 
    120   if (rows > 1 && rows < 20)
    121   {
    122     // Test matrix with NaN
    123     a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
    124     ComplexEigenSolver<MatrixType> eiNaN(a);
    125     VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
    126   }
    127 
    128   // regression test for bug 1098
    129   {
    130     ComplexEigenSolver<MatrixType> eig(a.adjoint() * a);
    131     eig.compute(a.adjoint() * a);
    132   }
    133 
    134   // regression test for bug 478
    135   {
    136     a.setZero();
    137     ComplexEigenSolver<MatrixType> ei3(a);
    138     VERIFY_IS_EQUAL(ei3.info(), Success);
    139     VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
    140     VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
    141   }
    142 }
    143 
    144 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
    145 {
    146   ComplexEigenSolver<MatrixType> eig;
    147   VERIFY_RAISES_ASSERT(eig.eigenvectors());
    148   VERIFY_RAISES_ASSERT(eig.eigenvalues());
    149 
    150   MatrixType a = MatrixType::Random(m.rows(),m.cols());
    151   eig.compute(a, false);
    152   VERIFY_RAISES_ASSERT(eig.eigenvectors());
    153 }
    154 
    155 EIGEN_DECLARE_TEST(eigensolver_complex)
    156 {
    157   int s = 0;
    158   for(int i = 0; i < g_repeat; i++) {
    159     CALL_SUBTEST_1( eigensolver(Matrix4cf()) );
    160     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
    161     CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );
    162     CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );
    163     CALL_SUBTEST_4( eigensolver(Matrix3f()) );
    164     TEST_SET_BUT_UNUSED_VARIABLE(s)
    165   }
    166   CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );
    167   s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
    168   CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );
    169   CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );
    170   CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );
    171 
    172   // Test problem size constructors
    173   CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));
    174   
    175   TEST_SET_BUT_UNUSED_VARIABLE(s)
    176 }